The distance protection of multi-terminal transmission lines need to be redesigned due to possible changes in the backup protection emanating from probable infeed currents produced from tapped transmission lines. Furthermore, high-resistance fault is another factor that relay become under-reach and cannot correctly identify the fault. In this study, an algorithm is presented based on synchrophasors. In this method, voltage and current signals of buses will be sent to system protection centre (SPC) and in SPC an algorithm based on active power calculation in buses is provided that is able to eliminate the effects of both mentioned factors. In this method, measurement or relay in tapped transmission line location are not required. The study includes analytical analysis and modelling and in modelling results a variety of faults with different fault resistances is considered. Two power systems including teed-feeder system and IEEE 14-bus power system are considered. The results show that in both power systems, and different types of faults, backup distance protection is improved. Simulations are conducted by Electro-Magnetic Transient Program works.